CAIE P3 2006 November — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2006
SessionNovember
TopicImplicit equations and differentiation

6 The equation of a curve is \(x ^ { 3 } + 2 y ^ { 3 } = 3 x y\).
  1. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { y - x ^ { 2 } } { 2 y ^ { 2 } - x }\).
  2. Find the coordinates of the point, other than the origin, where the curve has a tangent which is parallel to the \(x\)-axis.